Liquid cooling using interlayer microchannels has appeared as a viable and scalable packaging technology for 3-D multiprocessor system-on-chips (MPSoCs). Microchannel-based liquid cooling, however, can substantially increase the on-chip thermal gradients, which are undesirable for reliability, performance, and cooling efficiency. In this paper, we present GreenCool, an optimal design methodology for liquid-cooled 3-D MPSoCs. GreenCool simultaneously minimizes the cooling energy for a given system while maintaining thermal gradients and peak temperatures under safe limits. This is accomplished by tuning the heat transfer characteristics of the microchannels using channel width modulation. Channel width modulation is compatible with the current process technologies and incurs minimal additional fabrication costs. Through an extensive set of experiments, we show that channel width modulation is capable of complementing and enhancing the benefits of temperature-aware floorplanning. We also experiment with a 16-core 3-D system with stacked dynamic random-access memory, for which GreenCool improves energy efficiency by up to 53% with respect to no channel modulation.